|1/3-1/4|+|1/4-1/5|+.+|1/19-1/20|=

|1/3-1/4|+|1/4-1/5|+.+|1/19-1/20|=
|1/3-1/4|+|1/4-1/5|+.+|1/19-1/20|=

|1/3-1/4|+|1/4-1/5|+.+|1/19-1/20|=
|1/3-1/4|+|1/4-1/5|+.+|1/19-1/20|
=(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+...+(1/19-1/20)
=1/3-1/4+1/4-1/5+1/5-1/6+...1/19-1/20
=1/3-1/20
=17/60

17/60

其实绝对值符号是骗人的，都是大的减小的，所以绝对值符号可以不要，最后就变成了1/3-1/20，这有什么难呢，就等于17/60

17/60

17/60

原式=1/3-1/4+1/4-1/5+...-1/19+1/19-1/20
=1/3-1/20
=17/60